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Picking among several positions

Expected valueMedium

Your posterior gives states X, Y and Z the chances $\frac{1}{2}$ , $\frac{1}{4}$ and $\frac{1}{4}$ . Holding the full position loses $0$ , $8$ and $24$ in those states. Holding half loses $2$ , $7$ and $13$ . Closing out loses $5$ in every state. What is the expected loss of the best action? Give a number.

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Hint

Average each row over the posterior, then take the smallest.

Solution

Full position: $\frac{1}{4} \times 8 + \frac{1}{4} \times 24 = 8$ .
Half position: $\frac{1}{2} \times 2 + \frac{1}{4} \times 7 + \frac{1}{4} \times 13 = 6$ .
Closing out costs $5$ in every state, which is the smallest, so the answer is $5$ .

Answer: $5$

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